Q. 8.97 - Intermediate Algebra

Question

Simplify:

$\frac{\sqrt{64x^4{y}^5}}{\sqrt{2x{y}^3}}$

Step-by-Step Solution

Answer

The simplification of $\frac{\sqrt{64x^4{y}^5}}{\sqrt{2x{y}^3}}$ is $4xy\sqrt{3x}$

Step 1. Given

An expression $\frac{\sqrt{64x^4{y}^5}}{\sqrt{2x{y}^3}}$

To simplify the expression 

Step 2. Rewrite using the quotient property

Rewrite using the quotient property 

$\frac{\sqrt{64x^4{y}^5}}{\sqrt{2x{y}^3}}=\sqrt{\frac{64x^4{y}^5}{2x{y}^3}}$

Remove the common factors. 

                 $=\sqrt{48x^3{y}^2}$

Step 3. Rewrite the radical as the product of two radicals.

$\frac{\sqrt{64x^4{y}^5}}{\sqrt{2x{y}^3}}=\sqrt{48x^3{y}^2}$

                  $=\sqrt{16x^2{y}^2}\sqrt{3x}$

                 $=4xy\sqrt{3x}$

The simplification of the expression is $4xy\sqrt{3x}$